Sequential state discrimination with quantum correlation

Abstract

The sequential unambiguous state discrimination (SSD) of two states prepared in arbitrary prior probabilities is studied, and compared with three strategies that allow classical communication. The deviation from equal probabilities contributes to the success in all the tasks considered. When one considers at least one of the parties succeeds, the protocol with probabilistic cloning is superior to others, which is not observed in the special case with equal prior probabilities. We also investigate the roles of quantum correlations in SSD, and show that the procedure requires discords but rejects entanglement. The left and right discords correspond to the part of information extracted by the first observer and the part left to his successor respectively. Their relative difference is extended by the imbalance of prior probabilities.Keywords Sequential state discrimination · Entanglement · Discord IntroductionThe roles of quantum correlations in quantum information procedures is a fundamental problem in quantum information. These correlations have been widely investigated in various perspectives such as quantum entanglement [1], Bell nonlocality [2], and quantum discord [3,4]. One of the interesting findings in this field is that the algorithm for deterministic quantum computation with one qubit (DQC1) can surpass the performance of the corresponding classical ⋆ Quantum Information Processing (2018) 17:260

Discriminating bipartite mixed states by local operations

“…And the critical value s c approaches its maximum 3 − 2 √ 2, which is consistent with the result in Ref. [21]. According to Eqs.…”

“…[15] and demonstrated experimentally [19]. Further investigations on the optimized success probability of SSD with global measurements are reported for both the pure states [18,20,21] and mixed states [14].…”

“…Using a random search method [21], we can seek out the optimized success probability of SSD for both Bob and David. For fixed s, we have P f 1 ≤ 1/2.…”

“…P 2r2 ) corresponding to this optimal solution. In the former case, both of the mixed states are identified; while the latter case is considered to be one-state-identified because the success probability for identifying both |r1 r1| ⊗ |r ′ 1 r ′ 1 | and |r1 r1| ⊗ |r ′ 1 r ′ 1 | equals to zero [14,18,21]. If only one of |r1 r1| ⊗ |r ′ 1 r ′ 1 | and |r1 r1| ⊗ |r ′ 1 r ′ 1 | is neglected and the other one is identified, we say that the mixed state ρ1 is partially identified (e.g.…”

“…[14]. During the procedure of SSD, classical communications are forbidden [14,15,20,21]. This is essentially different from the local scheme where Bob's discrimination of the second particle is dependent on the premise that Alice communicates her failure result to him.…”